This mechanism of color confinement, combined with the `eigenvalue = location' interpretation, naturally resolves the issues (ii) and (iii).
For concreteness, let us consider a large-\(N\)  confining gauge theory with the first-order confinement/deconfinement transition,
e.g., 4d Yang-Mills on S\(^3\) .
To deconfine all colors, the energy of order \(N^2\)  is needed.
What if \(E\sim \epsilon N^2\) , where \(\epsilon \)  is of order \(N^0\)  but much smaller than 1?
Then the excitations coalesce to form an \(M\times M\)  block, where \(M\sim \sqrt{\epsilon }N\) .
This is because a large symmetry SU(\(N-M\) ) can be preserved in this way,
which leads to a large enhancement factor \({\rm vol}({\rm SU}(N-M))\) .
This SU(\(M\) )-partial-deconfinement [1]}, [2]}, [3]}
can occur both at weak- [4]} and strong-coupling regions [5]}.
In gauge/gravity duality, the partially-deconfined phase is a natural counterpart of the small black hole [1]}.
What if there are multiple excitations with smaller energy (say \(E\sim N^1\)  or \(N^0\) ), which are localized in separate locations in the emergent space (and, possibly, also in the spatial dimensions of QFT)?
Then each of them should clump to a small block in the color space, such that a large enhancement factor appears,
leading to the block-diagonal structure.
It is natural to regard each block as an extended object such as fundamental string or small black hole, that moves in the emergent space and interacts with others.
In the large-\(N\)  limit, various many-body states can be realized as configurations with multiple excited blocks.
The number of blocks and their sizes can take arbitrary values.
Therefore, the large-\(N\)  limit of gauge theory can serve as a second quantization of the gravity side.
